13. The Science of Energy: Chaps William Thomson's Dilemma

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13. The Science of Energy: Chaps 5-7 1. William Thomson's Dilemma Ho to reconcile Joule ith Carnot.

Joule: Heat can be converted into ork -- no "fall" required. Thomson's Conflicting Sympathies: Pro-Carnot: Absolute temp scale, melting point of ice.

1 13. The Science of Energy: Chaps William Thomson's Dilemma Ho to reconcile Joule ith Carnot.?!?!! Conflicting Claims: Carnot: Work produced by heat engines requires the fall of heat from to. Joule: Heat can be converted into ork -- no "fall" required. Thomson's Conflicting Sympathies: Pro-Carnot: Absolute temp scale, melting point of ice. Pro-Joule: Paddle heel explains fluid friction. Key Assumption of Thomson and Carnot: Any gain or loss of heat depends only on the initial and final states of a body, and not on the path beteen these states. This makes trouble for Joule's interconvertibility thesis:

2 Thomson's Thought Experiment (1848): Process #1: (Reversible compression and expansion producing ork.) Path A: Piston of cool air ith volume V 0 in initial state (1) is compressed so that temp rises to that of sea. Piston then plunged into sea. Path B: Under const temp, volume of air expands back to V 0 and pressure drops. Final state (3): greater temp/pressure, same volume as (1). Work done. Process #2: (Irreversible conduction producing no ork.) Path C: Piston of cool air ith volume V 0 in initial state (1) is plunged directly into sea. Temp rises via conduction to final state (3). No ork done. Pressure (2) B - volume increase - pressure decrease Process #1: Work done = area enclosed by ABC. (3) Process #2: No ork done. A - volume decrease - pressure increase C (1) - volume constant - pressure increase V 0 Volume

3 Upshot: To distinct processes that produce the same change of state. But only process #1 produces ork. What happened to the ork in process #2?" Big mystery if: (a) Same amount of heat is involved in both processes, and (b) Work cannot be created/destroyed, and (c) Heat and ork are interconvertible. Joule's response: Reject (a)! Allo that the amount of heat associated ith a process depends not on the initial and final states, but on the path taken beteen these states. Thomson is unpersuaded! harumph!

4 2. Thomson's (1849) "An Account of Carnot's Theory" Carnot's "Fundamental Principle": No heat is lost in the operation of a heat engine (recall ater analogy)." Concept of a "perfect thermo-dynamic engine": "A perfect thermo-dynamic engine is such that, hatever amount of mechanical effect it can derive from a certain thermal agency; if an equal amount be spent in orking it backards, an equal reverse thermal effect ill be produced." Call this a reversible heat engine. Q = heat in Q REV W = ork out Reverse it! REV W = ork in Q = heat out Q

5 Aside: Reversible vs irreversible processes A reversible process is a process minutely aay from equilibrium. Practical Check: To determine if a process is reversible, record it on video and run video backards. If the backards video represents something that's physically possible, then the process is reversible.! Example: Consider a frozen pond at 32 F.! air ice ater Process I: Air arms minutely. Ice melts sloly. Reversible! (Video check!) Reverse of Process I: Ice forms sloly. Air cools minutely. Process II: Air is heated quickly to 75 F. Ice melts rapidly. Irreversible! Backard video: Ice forms rapidly in 75 F eather causing air temperature to plummet!

6 Carnot Claim #1: The maximum efficiency of any heat engine is equal to that of a reversible engine operating beteen the same hot and s. Proof: Suppose e have a reversible engine A that produces ork W. Suppose there is a more efficient engine B beteen the same hot and cold places (B uses the same heat as A and produces more ork). No reverse A and hook it up to B. Q Q A W B W + Q Q

7 Carnot Claim #1: The maximum efficiency of any heat engine is equal to that of a reversible engine operating beteen the same hot and s. Proof: Suppose e have a reversible engine A that produces ork W. Suppose there is a more efficient engine B beteen the same hot and cold places (B uses the same heat as A and produces more ork). No reverse A and hook it up to B. Q Q A W B W + Q Q

8 Carnot Claim #1: The maximum efficiency of any heat engine is equal to that of a reversible engine operating beteen the same hot and s. Proof: Suppose e have a reversible engine A that produces ork W. Suppose there is a more efficient engine B beteen the same hot and cold places (B uses the same heat as A and produces more ork). No reverse A and hook it up to B. Engine (A+B) does ork for free (no net fall of heat required)! But, sez Carnot, this is impossible: a perpetual motion machine! A Q Q B = W Q Q A+B

9 Smith's Analysis: Carnot rejects the existence of perpetual motion machines based on empirical evidence (French enlightenment ideals). Thomson and Joule reject creation/destruction of vis-viva (ork) based on appeals to God (Christian metaphysical ideals). Thomson's concept of a perfect thermodynamic engine reflects Presbyterian imperatives: - standard of perfection (reversible ideal engines) to hich humans can only strive and aspire - imperfections (irreversible real engines) lie ith humans

10 3. Clausius Reforms Carnot (1850) "On the Moving Force of Heat" 1st Maxim (Joule's equivalence of ork and heat): "In all cases here ork is produced by heat, a quantity of heat proportional to the ork done is expended; and inversely, by the expenditure of a like quantity of ork, the same amount of heat may be produced." Rudolph Clausius Carnot's Assumption: In a heat engine, ork is produced by the transmission of heat from a to a, ith no loss/gain of heat as a result. Clausius: Accepts first clause as 2nd Maxim, but rejects second clause.! Consequences: Allos that the amount of heat associated ith a process depends on the path taken and not on the initial and final states. If Q in is the heat falling from the, and W is the ork produced, then the heat expended to the is Q out = Q in W. Q heat engine Q W W

11 Carnot Claim #2: In an ideal (i.e., reversible) heat engine, the ork produced depends only on the quantity of heat transmitted (i.e., the temperature of the hot and s), and not on the orking fluid. Clausius' Proof: Suppose A and B are reversible engines operating beteen the same hot and s, and A is more efficient (in the sense that B requires more heat to produce the same amount of ork that A produces). Reverse B and hook it up to A. Q Q + A W + B W + Q (W + ) Q + (W + )

12 Carnot Claim #2: In an ideal (i.e., reversible) heat engine, the ork produced depends only on the quantity of heat transmitted (i.e., the temperature of the hot and s), and not on the orking fluid. Clausius' Proof: Suppose A and B are reversible engines operating beteen the same hot and s, and A is more efficient (in the sense that B requires more heat to produce the same amount of ork that A produces). Reverse B and hook it up to A. Q Q + A W + B W + Q (W + ) Q + (W + )

13 Carnot Claim #2: In an ideal (i.e., reversible) heat engine, the ork produced depends only on the quantity of heat transmitted (i.e., the temperature of the hot and s), and not on the orking fluid. Clausius' Proof: Suppose A and B are reversible engines operating beteen the same hot and s, and A is more efficient (in the sense that B requires more heat to produce the same amount of ork that A produces). Reverse B and hook it up to A. Engine (A+B) takes an amount of heat from a to a ith no ork input! Q Q (W + ) A W + B Q + Q + (W + ) = A+B

Carnot Claim #2: In an ideal (i.e., reversible) heat engine, the ork produced depends only on the quantity of heat transmitted (i.e., the temperature of the hot and s), and not on the orking fluid.

14 Carnot Claim #2: In an ideal (i.e., reversible) heat engine, the ork produced depends only on the quantity of heat transmitted (i.e., the temperature of the hot and s), and not on the orking fluid. Clausius' Proof: Suppose A and B are reversible engines operating beteen the same hot and s, and A is more efficient (in the sense that B requires more heat to produce the same amount of ork that A produces). Reverse B and hook it up to A. Engine (A+B) takes an amount of heat from a to a ith no ork input! Clausius: This is impossible! "[Heat] everyhere exhibits the tendancy to annul differences of temperature, and therefore to pass from a armer body to a colder one." A+B

15 3. Thomson's ( ) "The Dynamical Theory of Heat" Prop. 1 (Joule): "When equal quantities of mechanical effect are produced by any means hatever from purely thermal sources, or lost in purely thermal effects, equal quantities of heat are put out of existence or are generated." Officially converts to Joule! But hat happens to ork during conduction or friction? Prop. 2 (Carnot & Clausius): "If an engine be such that, hen it is orked backards, the physical and mechanical agencies in every part of its motions are all reversed, it produces as much mechanical effect as can be produced by any thermodynamic engine, ith the same temperature of source and refrigerator, from a given quantity of heat." In other ords (Carnot Claim #1): The most efficient heat engine for any given hot and s is a reversible heat engine. Thomson no seeks a theological and cosmological foundation for Prop. 2 (isn't satisfied ith Carnot's or Clausius' reasoning).

16 Thomson on conduction and friction: "The fact is, it may I believe be demonstrated the ork is lost to man irrecoverably; but not lost in the material orld.... Although no destruction of energy can take place in the material orld ithout an act of poer possessed only by the supreme ruler, yet transformations take place hich remove irrecoverably from the control of man sources of poer hich, if the opportunity of turning them to his on account had been made use of, might have been rendered available." Smith's gloss: God has ordained for nature to basic las of energy: its conservation and its progressive transformation. Thomson: "Everything in the physical orld is progressive." Smith's gloss: Reflects a Presbyterian economy of nature. Energy = gift from God. Only God can restore it. Humans can transform it and distribute it, but in doing so lose some of it.

17 Thomson no claims: "It is impossible by means of inanimate material agency to derive mechanical effect from any portion of matter by cooling it belo the temperature of the coldest of the surrounding objects." In other ords: No heat engine can produce as its sole effect the complete conversion of heat to ork (there must be "exhaust" heat).

18 Thomson's Proof of Prop. 2: Let A and B be reversible engines ith same hot and s, and let A be more efficient (in the sense that A produces more ork than B for the same heat in). Reverse B and hook it up to A. Q Q A W + B W Q (W + ) Q W

19 Thomson's Proof of Prop. 2: Let A and B be reversible engines ith same hot and s, and let A be more efficient (in the sense that A produces more ork than B for the same heat in). Reverse B and hook it up to A. Q A W + Q B W Q (W + ) Q W

20 Thomson's Proof of Prop. 2: Let A and B be reversible engines ith same hot and s, and let A be more efficient (in the sense that A produces more ork than B for the same heat in). Reverse B and hook it up to A. Engine (A+B) converts heat to ork ith no exhaust. Q Q Q (W + ) A W B Q W = A+B

21 Three types of prohibited heat engines (a) Carnot: Work done ithout fall of heat (perpetual motion machine): (b) Clausius: Heat transfer from cold to ith no ork input: (c) Thomson: Conversion of heat to ork ith no exhaust: Aside: Prohibitions on (b) and (c) are knon today as the Clausius and Kelvin forms of the 2nd La, respectively.

4. Helmholtz, "Kraft", and Conservation of Energy Helmholtz (1847) "On the Conservation of Force": force ("kraft") = cause of motion vis viva = measure of force All causes of motion reduce to

22 4. Helmholtz, "Kraft", and Conservation of Energy Helmholtz (1847) "On the Conservation of Force": force ("kraft") = cause of motion vis viva = measure of force All causes of motion reduce to attractive/repulsive forces that depend on distances beteen point sources of matter. Conservation of force extends to all forces in nature. Herman von Helmholtz Thomson (1852): Appropriates Helmholtz's ideas in terms of "conservation of mechanical energy". Mechanical energy is measured by its effect (ork). The intensity of energy is represented by force (a potential gradient). "We may consequently regard it as certain that, neither by natural agencies of inanimate matter, nor by the operations arbitrarily efected by animated Creatures, can there be any change produced in the amount of mechanical energy in the Universe." Rankine (1853) rephrases this as "The la of the conservation of energy".

23 Cultural significance of ne "energy physics" British Association for the Advancement of Science (BAAS) meetings establish credibility of energy physics. Serves as unifying doctrine for BAAS members to rival Laplacian physics. Serves as patriotic and economic (steam engine technology) motivation for younger, entrepreneurial generation of BAAS members.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY SPRING 2007

MASSACHUSETTS INSTITUTE OF TECHNOLOGY SPRING 007 5.9 Energy Environment and Society (a Project Based First Year Subject supported by the d'arbeloff Program) ---------------------------------------------------------------------------------------